Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [checkerboard]

A puzzle involving checkerboards: grids of squares alternating black and white in color, most commonly an 8x8 board.

8
votes
1answer
345 views

How many total checkmates can you possibly make against the enemy king?

Just an interesting idea for a puzzle that I had So, I decided to see how many possible checkmate I could theoretically make, in a legal position that can be legally reached. Always assume that the ...
5
votes
3answers
139 views

What’s the most possible checkmates in one, but with no promoted pieces, in a position?

What is the most possible checkmates in one without promoted units in a position? It must all be legal, of course. Consider this a part two of this question: How many total checkmates can you ...
0
votes
1answer
181 views

Fastest Way To 6 Pawns On the B To H Files

MASSIVE UPDATE: I decided to play around with this again today, and I found MAJOR improvmemts for the B to G file games. See if you can beat me! If not, give proof as to why my game is optimal (To ...
6
votes
2answers
744 views

Chess with symmetric move-square

Every move in chess involves moving a piece to a square. Let us call this square the "move-square" for that turn. In the following, the move-square of the black player must be symmetrical (over the ...
14
votes
3answers
2k views

A Wacky, Wacky Chessboard (That Makes No Sense)

So yesterday I found this in the mail. A chessboard. But on the squares, things were written. Plaintext version: ...
4
votes
1answer
298 views

Chess Massacre Variants-Play Find The Fastest Way?

I have thought up several variations of massacre chess. Massacre chess is a game where almost every single move is a capture. The idea here is that only the chosen type of piece can capture. It ...
6
votes
3answers
147 views

Discrete Peaceful Encampments: Player 4 has entered the game!

Here's a variation of Discrete Peaceful Encampments: Player 3 has entered the game! (which itself is a variation of Peaceful Encampments). You have 3 white queens, 3 black queens, 3 red queens, and ...
5
votes
3answers
185 views

Discrete Peaceful Encampments: Player 3 has entered the game!

Here's a variation of Discrete Peaceful Encampments: 9 queens on a chessboard (which itself is a variation of Peaceful Encampments). You have 4 white queens, 4 black queens, and 4 red queens. Place ...
15
votes
4answers
1k views

Discrete Peaceful Encampments: 9 queens on a chessboard

Here's a discrete variation of yesterday's puzzle Peaceful Encampments. You have 8 white queens and 8 black queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no white ...
8
votes
1answer
315 views

A chess game with odd moves?

A friend and I like to play chess regularly. Like me, he is a lover of a good puzzle, which is what drew us to the game. The thrill of finding a checkmate in a board riddled with pieces cannot be ...
23
votes
7answers
5k views

Explore the square with 100 hops

This is a puzzle that was a fad when I was back in school. (It's not sooo long ago, but way before Smartphones with AngryBirds or DoodleJump came up...). For quite a while, everybody was scribbling ...
7
votes
3answers
4k views

Tiling a Chessboard with tetrominos

Is it possible to tile a $10\times10$ chessboard with (non-overlapping) T-tetrominos? If so, how? If not, prove it's impossible. Bonus: Which Tetris pieces can used to tile a 10$\times$10 ...
6
votes
1answer
364 views

The Knight Checker or Football Chess

Both Players uses 8 Knights on this chessboard game : The Knight Checker. All pieces starts in Rank 1 relative to players. White to move first. The Knight pieces makes regular moves as in a chess game ...
5
votes
1answer
231 views

A Battle of Dysfunctional Kings (Chess)

So recently I've learned about fairy chess and I've decided to write a puzzle based around the topic. Today's variation features a chess board which is missing eight squares (A1, A8, C3, C6, F3, F6, ...
6
votes
5answers
2k views

A chess board and a coin! [closed]

You have a standard chessboard, consisting of $64$ squares ($32$ white and $32$ black) each of dimensions $4\times4$ cm, and you have a standard coin of $2$ cm diameter with tail and head. You flip ...
2
votes
1answer
148 views

Row of alternating coin

I stumbled upon a mathematical puzzle that goes like this: You have 2n coins that alternate between head and tail. For example, if n=3, then it looks like H T H T H T, where H = head and T = tail. To ...
28
votes
1answer
3k views

How many queens can be on a chessboard without attacking each other?

What is the maximum number of queens that can be placed on a standard 8x8 chessboard such that no one of them is capable of attacking any of the others in a single move?
10
votes
2answers
181 views

make it to the top of the triangle

Suppose you have a triangle that extends infinitely downwards, with circles inside, arranged in this arrangement: ...
11
votes
3answers
2k views

The knight's game

Alice and Bob play the following game on a standard $8\times8$ chessboard. In the very beginning, Alice picks a square on the chessboard and places a knight on this square. Then Bob and Alice ...
27
votes
3answers
4k views

16 pawns on a chess board with no three collinear: how do I go about solving this?

Here's a problem that was posed to me but I haven't seen anything about it anywhere online! I'm beginning to wonder if I'm just getting played! You have a chessboard and sixteen pawns. The puzzle is ...
7
votes
1answer
144 views

Permuting rows and columns to switch white rooks with black rooks

An adversary places eight white rooks and eight black rooks on sixteen squares of a chessboard, subject to these rules: In any row, there must be exactly two rooks, one of each color. In any column, ...
5
votes
3answers
254 views

Crazy queen in checkers

Checkers Checkers, also called draughts, is an interesting game. all pieces are placed on black tile and are all pawns at the start. When a pawn reach the final line, a powerful piece is created: the ...
10
votes
1answer
373 views

Lights out game on a chessboard

Alice and Bob play a game with an 8×8 grid of lights, all initially on. They take turns choosing a light which is on and turning it off, with Alice going first. However, the grid is rigged such that ...
7
votes
2answers
2k views

How many Queens and Knights does it take to cover a chessboard?

Given an 8x8 chessboard, your goal is to "cover" each space on the board. A space is "covered" if there is a piece on it, or if a piece on the board can be moved to that space in one move. If you ...
11
votes
4answers
267 views

Checkerboard Infection Variant

There is an insidious virus (less contagious than C. Coli, but still dangerous) which plagues the squares of checkerboards. This virus spreads through social interaction: whenever the majority of a ...
25
votes
4answers
2k views

Lions and Zebras on a Chess Board

The black knight is our lion chasing 8 white bishop zebras which can't capture. Can the zebras evade the lion forever, if team zebra positions all the pieces and has the first turn? Rules: The game ...
8
votes
2answers
319 views

Covering a chessboard with L-tetrominoes

We all know the classic puzzle of trying to tile a mutilated chessboard with $2\times1$ dominoes. Let's imagine that, instead of dominoes, we have $n^2$ L-shaped tetrominoes and we want to tile a $2n\...
1
vote
2answers
242 views

The Monster and the Chessboard [duplicate]

You have a standard checkerboard with 64 squares and a coin in each square, randomly facing heads or tails up. There is an evil monster in the room with you and he arbitrarily selects some square and ...
26
votes
7answers
8k views

Two Knights, two Bishops, two Rooks and two Kings on a 4x4 chessboard

Place two Knights, two Rooks, two Bishops and two Kings on a 4x4 chessboard, so that: 1) The Kings are not attacked at all. 2) All other pieces are attacked exactly once. Ignore color, so every ...
3
votes
2answers
206 views

Is it possible to pack the tetrominoes exactly on the checkboard?

I have this as an exercise but I'm not sure what's the best way to approach it. I've tried the pack them but wasn't able to do so. I see that having them combined will yield in 10 whites and 10 blacks ...
19
votes
4answers
4k views

Chessboard Rook Problem

Let's say that you have a chessboard (they are 8x8 spaces) with a rook on it (only moves horizontally & vertically). You can put walls horizontally or vertically between the spaces. If the rook ...
4
votes
3answers
906 views

Total no of squares on a Chess Board

Is there any formula than calculates the total number of squares on chessboard? For example in a $8\times8$ chessboard, there are squares of sizes $1\times1$, $2\times2$, $\ldots$, $8\times8$. So I ...
36
votes
3answers
5k views

The coolest checkerboard magic trick

In the small town of Terni (Italy), there's a couple of young friends named Marco and Leonardo, who like to perform magic tricks to a restricted audience of common friends and relatives. They like to ...
1
vote
1answer
156 views

King of Captures

The player's black King (above) is about to capture the remaining opponent pieces as continuation of his move and 10 white pieces have already been captured on the same turn/move. What is the position ...
-3
votes
1answer
154 views

How many positions can the queen control? [closed]

Given the size of board (n) and the position of the queen (r,c) how can we calculate the total number of squares which can be controlled by the queen?
3
votes
1answer
672 views

Can more than 24 knights of each color be placed on a chessboard without any pieces attacking opposite color?

The maximal number of knights of a single color that can be placed on a chessboard without any knight being one knights-move away from any other is 32; such a position may easily be achieved by ...
28
votes
4answers
11k views

How many chess pieces does it take to “cover” all spaces on a chessboard?

Given an 8x8 chessboard, your goal is to "cover" each space on the board with the fewest possible number of pieces. A space is "covered" if there is a piece on it, or if a piece on the board can be ...
7
votes
4answers
310 views

No Square Allowed

On a Chessboard, place as many chess pieces as you can. Position the center of each piece on the center of a square. Avoid placing any 4 pieces at the corners of a square (even a tilted square). ...
-1
votes
1answer
217 views

Colouring an n times n grid using n colours

Inspired by the four colours puzzle. The goal is to color the squares of an $n\times n$ grid with $n$ colors such that All squares are coloured. no two squares of the same color touch at an edge or ...
6
votes
3answers
2k views

Coloring an n by n grid with four colors

This is a generalization of Place 4x12 detainees on a 7x7 grid of cells. The goal is to color the squares of an $n\times n$ grid with four colors such that at most one square is uncolored no two ...
9
votes
3answers
266 views

The Flea Circuit

Starting on a square of the checkerboard, "The Flea" is trained to jump to the center of another square. Then it keeps jumping (center to center) from square to square all around the board. It is ...
8
votes
5answers
632 views

Professor Halfbrain's infinite chessboard theorems

After his first set of theorems involving queen-accessibility, Professor Halfbrain started wondering about infinite chessboards rather than just ones with arbitrary large dimensions. He came up with ...
23
votes
1answer
543 views

The life of a Knight: Conway style

So I was thinking about Conway's game of life and the ridiculous kinds of patterns that can be made (Things that move across infinite space etc) and then I thought, hey could a chess knight do this as ...
8
votes
2answers
781 views

Eight queens on the chessboard with mirrors

A 8-by-8 chessboard has two mirrors added on its left and right margin. The mirrors reflect the queen moves so that a queen threatens additional squares on the board. A queen threatens all squares in ...
10
votes
1answer
568 views

Let's revisit this later (a two player knight's game)

Alice and Bob play a game on the following irregular chessboard. (Note the blacked out squares are not legal moves.) Alice starts the game by placing a knight on any square she chooses. They then ...
20
votes
2answers
1k views

Desegregate the Knights

You are given a 3 by 3 chessboard with a knight on each corner, where the knights in the top row are black and in the bottom row are white. On each turn, you may move a knight of either color (the ...
6
votes
1answer
156 views

Knight on a rectangular chessboard

On a rectangular $ 4 \times 2016 $ chessboard, a knight begins in the lower left corner, makes several knight moves, visits all squares of the chessboard at least once and in the end returns to the ...
7
votes
1answer
263 views

Least amount of moves is required

You have 8x8 board and 9 identical pieces placed in a 3x3 square at the bottom left corner of the board. You are going to play a very simple game. Your task is to move these 9 pieces to the 3x3 square ...
5
votes
3answers
373 views

Place 16 queens in a $16\times 16$ board peacefully, also in subboards!

What is the smallest number, $n$ in which $n$ queens can live in a $n\times n$ board peacefully? Of course not more than 8. ☺ (read about the eight queen puzzle) But this was not the question. ...
10
votes
1answer
153 views

Combinatorial Agriculture, part 2

Your 64 acre square farm has been doing well and you decide to expand with an orchard. The orchard is also in the form of an 8-by-8 square of subplots, each of which can hold one tree. You have 3 each ...